Hi all, I am having hard time in solving the following non-linear elliptic equation numerically for u:
$$(\eta+u) \bigg((\eta+u)^2 -\frac{\varphi ^2}{4} \bigg)\nabla^2 u -\frac{\varphi^2}{4} \partial _m \bigg ( \frac{\eta+u-1}{ \varphi} \bigg) \times \partial ^m \bigg ( \frac{\eta+u+1}{ \varphi} \bigg) = 0$$
This is (3.31) equation of the following paper: http://arxiv.org/pdf/0907.1151v2.pdf
I tried to edit it. Hope this is the convenient form.
